Precalculus Examples

Step 1
Consider the corresponding sign chart.
Step 2
Use the sign chart and the given matrix to find the cofactor of each element.
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Calculate the minor for element .
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Consider the determinant with the row and column deleted.
Evaluate the determinant.
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The determinant of a matrix can be found using the formula .
Simplify the determinant.
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Simplify each term.
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Multiply by .
Multiply by .
Subtract from .
Calculate the minor for element .
Tap for more steps...
Consider the determinant with the row and column deleted.
Evaluate the determinant.
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Subtract from .
Calculate the minor for element .
Tap for more steps...
Consider the determinant with the row and column deleted.
Evaluate the determinant.
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Subtract from .
Calculate the minor for element .
Tap for more steps...
Consider the determinant with the row and column deleted.
Evaluate the determinant.
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Subtract from .
Calculate the minor for element .
Tap for more steps...
Consider the determinant with the row and column deleted.
Evaluate the determinant.
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Subtract from .
Calculate the minor for element .
Tap for more steps...
Consider the determinant with the row and column deleted.
Evaluate the determinant.
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Subtract from .
Calculate the minor for element .
Tap for more steps...
Consider the determinant with the row and column deleted.
Evaluate the determinant.
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Subtract from .
Calculate the minor for element .
Tap for more steps...
Consider the determinant with the row and column deleted.
Evaluate the determinant.
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Subtract from .
Calculate the minor for element .
Tap for more steps...
Consider the determinant with the row and column deleted.
Evaluate the determinant.
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Subtract from .
The cofactor matrix is a matrix of the minors with the sign changed for the elements in the positions on the sign chart.
Step 3
Transpose the matrix by switching its rows to columns.
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